The X-ray transform on asymptotically conic spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929522536873984 |
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| author | Vasy, András Zachos, Evangelie |
| author_facet | Vasy, András Zachos, Evangelie |
| contents | In this paper, partly based on Zachos' PhD thesis, we show that the geodesic X-ray transform is stably invertible near infinity on a class of asymptotically conic manifolds which includes perturbations of Euclidean space. In particular certain kinds of conjugate points are allowed. Further, under a global convex foliation condition, the transform is globally invertible.
The key analytic tool, beyond the approach introduced by Uhlmann and Vasy, is the introduction of a new pseudodifferential operator algebra, which we name the 1-cusp algebra, and its semiclassical version. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_11706 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The X-ray transform on asymptotically conic spaces Vasy, András Zachos, Evangelie Differential Geometry Analysis of PDEs 53C65 (Primary) 35S05 (Secondary) In this paper, partly based on Zachos' PhD thesis, we show that the geodesic X-ray transform is stably invertible near infinity on a class of asymptotically conic manifolds which includes perturbations of Euclidean space. In particular certain kinds of conjugate points are allowed. Further, under a global convex foliation condition, the transform is globally invertible. The key analytic tool, beyond the approach introduced by Uhlmann and Vasy, is the introduction of a new pseudodifferential operator algebra, which we name the 1-cusp algebra, and its semiclassical version. |
| title | The X-ray transform on asymptotically conic spaces |
| topic | Differential Geometry Analysis of PDEs 53C65 (Primary) 35S05 (Secondary) |
| url | https://arxiv.org/abs/2204.11706 |